Question

Gas at constant T and P is contained in a supply line connected
through a valve to aclosed tank containing the same gas at a lower
pressure. The valve is opened to allowflow of gas into the tank,
and then is shut again.
(a) Develop a general equation relating n1 and n2,the moles (or
mass) of gas in the tank at the beginning and end of the process,
to the properties U1 and U2,
the internalenergy of the gas in the tank at the beginning and end
of the process, and
H',theenthalpy of the gas in the supply line, and to Q,the heat
transferred to the materialin the tank during the process.
(b) Reduce the general equation to its simplest form for the
special case of an ideal gaswith constant heat capacities.
(c) Further reduce the equation of (b) for the case of nl =
0.
(d)Further reduce the equation of (c)for the case in which, in
addition,Q =0.
(e)Treating nitrogen as an ideal gas for which Cp = (7/2)R,
apply the appropriateequation to the case in which a steady supply
of nitrogen at
298.15K (25°C) and 3 bar flows into an evacuated tank of 4-m3
volume, and calculate the moles of nitrogenthat flow into the tank
to equalize the pressures for two cases:
1.
Assume that no heat
flows
from the gas to the tank or through the tank walls.
2.
The tank weighs
400
kg, is perfectly insulated, has an initial temperature of
298.15K (25"C), has a specific heat of 0.46 kJ kgp1 K-',
and is heated by thegas so as always to be at the temperature of
the gas in the tank.